Adjoint fermion zero-modes for SU(N) calorons

Abstract

We derive analytic formulas for the zero-modes of the Dirac equation in the adjoint representation in the background field of Q=1 SU(N) calorons. Solutions with various boundary conditions are obtained, including the physically most relevant cases of periodic and antiperiodic ones. The latter are essential ingredients in a semiclassical treatment of finite temperature supersymmetric Yang-Mills theory. A detailed discussion of adjoint zero-modes in several other contexts is also presented.

40 latex pages and 5 eps figures

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• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Conformality or confinement (II): One-flavor CFTs and mixed-representation QCD
• The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum
• Anderson Localization in high temperature QCD: background configuration properties and Dirac eigenmodes
• The gaugino condensate from asymmetric four-torus with twists
• The Vortex Structure of SU(2) Calorons
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• The thermal instanton determinant in compact form
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD
• A Closer Look at Gluons
• Caloron correction to the effective potential in thermal gluodynamics
• Memory efficient finite volume schemes with twisted boundary conditions